Asif123 wrote:
In 1982 a certain company had losses of $10,000 per month. In the first three months of 1983, this company had gains of $4,000 per month. On the average, what would the company need to gain per month in the remainder of 1983 in order to break even over this two-year period?
(A) $9,000 (B) $10,800 (C) $12,000 (D) $13,500 (E) $18,000
Overall average profit in the 24 months = 0 (since the company breaks even) => Sum of profits = 0 * 12 = 0
Average loss in the first 12 months = $10000 => Loss = - 10000 * 12
Average profit in the next 3 months = $4000 => Profit = + 4000 * 3
We need to determine the average profit in the next 9 months
For the sum to be ZERO, we must have profit of (12 * 10000 - 3 * 4000) = $108000 in the last 9 months
=> Average profit in the last 9 months = $108000/9 = $12000
Answer CAlternative approach:
We have the following information:
\(\[
\begin{matrix}
# months & Average profit/loss \\
12 & -$10000 \\
3 & $4000\\
9 & $x
\end{matrix}
\]\)
Take ratio of the months (frequencies) for ease of calculation:
\(\[
\begin{matrix}
# months & Average profit/loss \\
4 & -$10000 \\
1 & $4000\\
3 & $x
\end{matrix}
\]\)
Since the company breaks even, the total profit/loss after 24 months is ZERO, and hence, the average is ZERO. Thus, we have:
[4 * (-10000) + 1 * 4000 + 3x]/[4 + 1 + 3] = 0
=> x = $12000
Answer C